In this paper, we tackle the challenging problem of 3D keypoint estimation of
general objects using a novel implicit representation. Previous works have
demonstrated promising results for keypoint prediction through direct
coordinate regression or heatmap-based inference. However, these methods are
commonly studied for specific subjects, such as human bodies and faces, which
possess fixed keypoint structures. They also suffer in several practical
scenarios where explicit or complete geometry is not given, including images
and partial point clouds. Inspired by the recent success of advanced implicit
representation in reconstruction tasks, we explore the idea of using an
implicit field to represent keypoints. Specifically, our key idea is employing
spheres to represent 3D keypoints, thereby enabling the learnability of the
corresponding signed distance field. Explicit keypoints can be extracted
subsequently by our algorithm based on the Hough transform. Quantitative and
qualitative evaluations also show the superiority of our representation in
terms of prediction accuracy.

本研究采用新颖的隐式表示方法解决了通用物体的 3D 关键点估计问题，通过使用球来表示 3D 关键点，以此实现对应的带符号距离场的可学习性，并基于 Hough 变换后提取出显式的关键点。实验结果表明，该表示方法在预测精度方面具有优越性。

使用隐式表示学习进行 3D 关键点估计

3D Keypoint Estimation Using Implicit Representation Learning

Normalizing flows are a powerful tool for building expressive distributions
in high dimensions. So far, most of the literature has concentrated on learning
flows on Euclidean spaces. Some problems however, such as those involving
angles, are defined on spaces with more complex geometries, such as tori or
spheres. In this paper, we propose and compare expressive and numerically
stable flows on such spaces. Our flows are built recursively on the dimension
of the space, starting from flows on circles, closed intervals or spheres.

本文研究在高维度空间中建立表现力强的分布，提出了计算表达稳定的 Lipschitz normalizing flows，探讨圆、封闭区间或球面上流的性能，并使用实验结果验证其有效性。